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Arithmetic Brownian motion and real options

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  • Alexander, David Richard
  • Mo, Mengjia
  • Stent, Alan Fraser

Abstract

We treat real option value when the underlying process is arithmetic Brownian motion (ABM). In contrast to the more common assumption of geometric Brownian motion (GBM) and multiplicative diffusion, with ABM the underlying project value is expressed as an additive process. Its variance remains constant over time rather than rising or falling along with the project’s value, even admitting the possibility of negative values. This is a more compelling paradigm for projects that are managed as a component of overall firm value. After outlining the case for ABM, we derive analytical formulas for European calls and puts on dividend-paying assets as well as a numerical algorithm for American-style and other more complex options based on ABM. We also provide examples of their use.

Suggested Citation

  • Alexander, David Richard & Mo, Mengjia & Stent, Alan Fraser, 2012. "Arithmetic Brownian motion and real options," European Journal of Operational Research, Elsevier, vol. 219(1), pages 114-122.
    • Handle: RePEc:eee:ejores:v:219:y:2012:i:1:p:114-122
    DOI: 10.1016/j.ejor.2011.12.023
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    Cited by:

    1. Glensk, Barbara & Madlener, Reinhard, 2017. "Evaluating the Enhanced Flexibility of Lignite-Fired Power Plants: A Real Options Analysis," FCN Working Papers 107/2016, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    2. Pedro Godinho, 2015. "Estimating State-Dependent Volatility of Investment Projects: A Simulation Approach," GEMF Working Papers 2015-02, GEMF, Faculty of Economics, University of Coimbra.
    3. Barbara Glensk & Reinhard Madlener, 2019. "Energiewende @ Risk: On the Continuation of Renewable Power Generation at the End of Public Policy Support," Energies, MDPI, vol. 12(19), pages 1-25, September.
    4. Glensk, Barbara & Madlener, Reinhard, 2015. "Real Options Analysis of the Flexible Operation of an Enhanced Gas-Fired Power Plant," FCN Working Papers 11/2015, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    5. Seiji Harikae & James S. Dyer & Tianyang Wang, 2021. "Valuing Real Options in the Volatile Real World," Production and Operations Management, Production and Operations Management Society, vol. 30(1), pages 171-189, January.
    6. Ernesto Garnier and Reinhard Madlener, 2016. "The Influence of Policy Regime Risks on Investments in Innovative Energy Technology," The Energy Journal, International Association for Energy Economics, vol. 0(Bollino-M).
    7. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2020. "Early exercise boundaries for American-style knock-out options," European Journal of Operational Research, Elsevier, vol. 285(2), pages 753-766.
    8. Sesana, Debora & Marazzina, Daniele & Fusai, Gianluca, 2014. "Pricing exotic derivatives exploiting structure," European Journal of Operational Research, Elsevier, vol. 236(1), pages 369-381.
    9. Glensk, Barbara & Madlener, Reinhard, 2019. "The value of enhanced flexibility of gas-fired power plants: A real options analysis," Applied Energy, Elsevier, vol. 251(C), pages 1-1.
    10. Kyungwon Kim & Jae Wook Song, 2020. "Detecting Possible Reduction of the Housing Bubble in Korea for Different Residential Types and Regions," Sustainability, MDPI, vol. 12(3), pages 1-31, February.
    11. Pedro Godinho, 2015. "Estimating State-Dependent Volatility of Investment Projects: A Simulation Approach," GEMF Working Papers 2015-02, GEMF, Faculty of Economics, University of Coimbra.
    12. Castellini, Marta & Menoncin, Francesco & Moretto, Michele & Vergalli, Sergio, 2021. "Photovoltaic Smart Grids in the prosumers investment decisions: a real option model," Journal of Economic Dynamics and Control, Elsevier, vol. 126(C).
    13. Brandão, Luiz E. & Fernandes, Gláucia & Dyer, James S., 2018. "Valuing multistage investment projects in the pharmaceutical industry," European Journal of Operational Research, Elsevier, vol. 271(2), pages 720-732.
    14. Carol Alexander & Xi Chen, 2021. "Model risk in real option valuation," Annals of Operations Research, Springer, vol. 299(1), pages 1025-1056, April.
    15. Trigeorgis, Lenos & Tsekrekos, Andrianos E., 2018. "Real Options in Operations Research: A Review," European Journal of Operational Research, Elsevier, vol. 270(1), pages 1-24.
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